Elliptic curve data - 15210.k3

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• ec_curvedata •

  Column	Type
  Ciso	text
  Clabel	text
  Cnumber	smallint
  abc_quality	double precision
  absD	numeric
  adelic_genus	integer
  adelic_index	integer
  adelic_level	bigint
  ainvs	numeric[]
  analytic_rank	smallint
  bad_primes	integer[]
  class_deg	smallint
  class_size	smallint
  cm	smallint
  conductor	integer
  degree	bigint
  elladic_images	text[]
  faltings_height	numeric
  faltings_index	smallint
  faltings_ratio	smallint
  intrinsic_torsion	smallint
  iso_nlabel	smallint
  isogeny_degrees	smallint[]
  jinv	numeric[]
  lmfdb_iso	text
  lmfdb_label	text
  lmfdb_number	smallint
  manin_constant	smallint
  min_quad_twist_ainvs	numeric[]
  min_quad_twist_disc	smallint
  modell_images	text[]
  modm_images	text[]
  nonmax_primes	smallint[]
  nonmax_rad	integer
  num_bad_primes	smallint
  num_int_pts	integer
  optimality	smallint
  potential_good_reduction	boolean
  rank	smallint
  regulator	numeric
  semistable	boolean
  serre_invariants	integer[]
  sha	integer
  sha_primes	smallint[]
  signD	smallint
  squarefree_disc	boolean
  stable_faltings_height	numeric
  szpiro_ratio	double precision
  torsion	smallint
  torsion_primes	smallint[]
  torsion_structure	smallint[]

  
  {'Ciso': '15210n', 'Clabel': '15210n6', 'Cnumber': 6, 'abc_quality': 1.0522127879225598, 'absD': 31668693849000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 1560, 'ainvs': [1, -1, 0, -507285, 138930741], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 15210, 'degree': 221184, 'elladic_images': ['2.6.0.1', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0493732180012022393049926001', 'prec': 97}, 'faltings_index': 5, 'faltings_ratio': 6, 'intrinsic_torsion': 1, 'iso_nlabel': 10, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [4102915888729, 9000000], 'lmfdb_iso': '15210.k', 'lmfdb_label': '15210.k3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -334, -2368], 'min_quad_twist_disc': -39, 'modell_images': ['2Cs', '3B'], 'modm_images': ['2.6.0.a.1', '3.4.0.a.1', '6.24.0.a.1', '12.48.0.a.1', '24.96.1.cp.2', '39.8.0-3.a.1.1', '40.12.0.a.1', '52.12.0-2.a.1.1', '60.96.1.h.3', '78.48.0.?', '120.192.5.?', '156.96.0.?', '312.192.1.?', '520.24.0.?', '780.192.1.?', '1560.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 1521], [3, 8, 169], [5, 6, 3042], [13, 86, 90]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.21759239493637902558062626085', 'prec': 97}, 'szpiro_ratio': 5.2986120518611965, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
• ec_classdata •

  Column	Type
  anlist	smallint[]
  aplist	smallint[]
  class_deg	smallint
  class_size	smallint
  conductor	integer
  isogeny_matrix	smallint[]
  lmfdb_iso	text
  trace_hash	bigint

  
  {'anlist': [0, 1, -1, 0, 1, -1, 0, 4, -1, 0, 1, 0, 0, 0, -4, 0, 1, -6, 0, 4, -1], 'aplist': [-1, 0, -1, 4, 0, 0, -6, 4, 0, 6, -8, -2, -6, -4, 0, 6, 0, -10, 4, 0, -2, 8, 12, 18, -2], 'class_deg': 12, 'class_size': 8, 'conductor': 15210, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '15210.k', 'trace_hash': 1348567361393527049}
• ec_mwbsd •

  Column	Type
  area	numeric
  conductor	integer
  gens	numeric[]
  heights	numeric[]
  lmfdb_label	text
  ngens	smallint
  rank_bounds	smallint[]
  real_period	numeric
  sha_an	numeric
  special_value	numeric
  tamagawa_product	integer
  torsion_generators	numeric[]
  xcoord_integral_points	numeric[]

  
  {'area': {'__RealLiteral__': 0, 'data': '0.016593463337770595687997863959', 'prec': 97}, 'conductor': 15210, 'gens': [], 'heights': [], 'lmfdb_label': '15210.k3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.37098238033420191849979723322', 'prec': 97}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 97}, 'special_value': {'__RealLiteral__': 0, 'data': '1.4839295213368076739991889328695723739', 'prec': 127}, 'tamagawa_product': 64, 'torsion_generators': [[-822, 411, 1], [426, -213, 1]], 'xcoord_integral_points': [-822, 426]}
• ec_iwasawa •

  Column	Type
  iwdata	jsonb
  iwp0	smallint
  lmfdb_label	text

  
  {'iwdata': {'2': [3, 0], '3': 'a', '5': [0, 0], '13': 'a'}, 'iwp0': 5, 'lmfdb_label': '15210.k3'}
• ec_torsion_growth •

  Column	Type
  degree	smallint
  field	numeric[]
  lmfdb_label	text
  torsion	smallint[]

  
  
  • id: 781907
    {'degree': 2, 'field': [-3, -1, 1], 'lmfdb_label': '15210.k3', 'torsion': [2, 6]}
  • id: 781909
    {'degree': 4, 'field': [3, 18, -17, -2, 1], 'lmfdb_label': '15210.k3', 'torsion': [2, 12]}
  • id: 781908
    {'degree': 4, 'field': [94, -34, 35, -2, 1], 'lmfdb_label': '15210.k3', 'torsion': [2, 4]}
  • id: 781910
    {'degree': 4, 'field': [484, 0, 34, 0, 1], 'lmfdb_label': '15210.k3', 'torsion': [2, 4]}
  • id: 781911
    {'degree': 6, 'field': [192, 0, 0, -27, 0, 0, 1], 'lmfdb_label': '15210.k3', 'torsion': [2, 6]}
  • id: 781912
    {'degree': 8, 'field': [49, -210, 436, -482, 317, -94, 36, -4, 1], 'lmfdb_label': '15210.k3', 'torsion': [2, 12]}
  • id: 781913
    {'degree': 8, 'field': [519, -492, 592, -184, 53, 44, -10, -4, 1], 'lmfdb_label': '15210.k3', 'torsion': [2, 12]}
  • id: 781914
    {'degree': 12, 'field': [1200, 360, 1152, -2490, 45, 1080, 187, -366, -30, 70, -3, -6, 1], 'lmfdb_label': '15210.k3', 'torsion': [6, 6]}
  • id: 781917
    {'degree': 16, 'field': [-1797, 32640, -62724, 19416, 122884, -234728, 174296, -25944, -56159, 30008, 4972, -5008, 46, 336, -28, -8, 1], 'lmfdb_label': '15210.k3', 'torsion': [2, 24]}
  • id: 781915
    {'degree': 16, 'field': [2521, -16624, 82702, -109900, 7448, 35840, 18690, -17716, -4699, 3856, 1134, -644, -196, 112, 4, -8, 1], 'lmfdb_label': '15210.k3', 'torsion': [4, 12]}
  • id: 781916
    {'degree': 16, 'field': [13459486, 8280304, -5383014, -5028364, 723701, 1809858, -72332, -390302, 21762, 42736, -1208, -3426, 116, 182, -6, -8, 1], 'lmfdb_label': '15210.k3', 'torsion': [2, 8]}
  • id: 781918
    {'degree': 16, 'field': [45631836, -327170016, 515939760, 283076640, 73543374, 58089744, 10438512, 3393120, 1169491, 73144, 76832, -4512, 4034, -432, 116, -8, 1], 'lmfdb_label': '15210.k3', 'torsion': [2, 8]}
  • id: 781919
    {'degree': 18, 'field': [-17859, -1036431, -348795, 726198, 893304, -522666, -302008, 92514, 120003, -34951, -26283, 11202, 2058, -1236, -264, 160, 3, -9, 1], 'lmfdb_label': '15210.k3', 'torsion': [2, 18]}
• ec_localdata •

  Column	Type
  conductor	integer
  conductor_valuation	smallint
  discriminant_valuation	smallint
  j_denominator_valuation	smallint
  kodaira_symbol	smallint
  lmfdb_label	text
  prime	integer
  reduction_type	smallint
  root_number	smallint
  tamagawa_number	smallint

  
  
  • id: 336255
    {'conductor': 15210, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '15210.k3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 336256
    {'conductor': 15210, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '15210.k3', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
  • id: 336257
    {'conductor': 15210, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '15210.k3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
  • id: 336258
    {'conductor': 15210, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '15210.k3', 'prime': 13, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
• ec_galrep •

  Column	Type
  adelic_gens	bigint[]
  adelic_image	text
  conductor	integer
  elladic_image	text
  lmfdb_label	text
  modell_image	text
  prime	smallint

  
  
  • id: 1765306
    {'adelic_gens': [[1273, 234, 26, 1325], [781, 1092, 1326, 313], [937, 1092, 234, 1327], [1549, 12, 1548, 13], [1, 12, 0, 1], [1, 0, 12, 1], [9, 4, 1544, 1553], [937, 1326, 0, 1], [479, 0, 0, 1559]], 'adelic_image': '1560.384.5.?', 'conductor': 15210, 'lmfdb_label': '15210.k3', 'prime': 0}
  • id: 71884
    {'conductor': 15210, 'elladic_image': '2.6.0.1', 'lmfdb_label': '15210.k3', 'modell_image': '2Cs', 'prime': 2}
  • id: 71885
    {'conductor': 15210, 'elladic_image': '3.4.0.1', 'lmfdb_label': '15210.k3', 'modell_image': '3B', 'prime': 3}
• lmfdb_iso 15210.k does not appear in ec_padic